effective length for axial stress for steel column

huangyhg

effective length for axial stress for steel column
i have a situation in which i am looking at combined flexural and axial stresses on a large base supported spire (+200 ft).  it's similar to a flagpole (without the flag), so i have already reviewed the criteria set forth in ansi/naam fp1001-07.  however, i also want to cross-check my numbers with aisc 13th edition.
in doing so, to calculate the allowable axial load i have concern with the selection for my unbraced length/height.  in a scenario in which i have just one cross section, i would use the full height of the column and a k=2.1 (for fixed base, free top).  however, my condition telescopes down in size over the height of the spire.  i don't think using the segment length for the unbraced height would be correct since the splice joints aren't braced.  my thought is to utilize the height of the spire above the splice joint for the section in question (i.e. if top section was 50' long, use 50'; for the next 50' segment, use 100'...and the base section would utilize the full height).
i have run both scenarios and the numbers i get using the cumulative unbraced length method i mention seem to produce similar numbers to the fp1001-07 document, so this seems justified.  
any thoughts/recommendations?
nick deal, p.e.
michael brady inc.
i use bs codes but this sound like the way i would do it.
i would check the base section first and get max. moments based in effective length 2.0l. the moment diagram will curve from here to the top of the pole so even if you were to proportion the applied moment you would have a conservative figure at each section.
the capacity should be checked for combined bending and axial.
"in doing so, to calculate the allowable axial load i have concern with the selection for my unbraced length/height.  in a scenario in which i have just one cross section, i would use the full height of the column and a k=2.1 (for fixed base, free top)."
agreed  
"however, my condition telescopes down in size over the height of the spire.  i don't think using the segment length for the unbraced height would be correct since the splice joints aren't braced."
definitely would be very wrong to use just hte segment length.
"my thought is to utilize the height of the spire above the splice joint for the section in question (i.e. if top section was 50' long, use 50'; for the next 50' segment, use 100'...and the base section would utilize the full height)."
the problem with this approach is deciding on k for these upper portions.  k will be very much larger than 2.1 for these.  i honestly don't even know of a good way to start trying to come up with it.
you might consider using the aisc app. 7 direct analysis method for this problem.  it does away with the k factor which is very difficult to *correctly* determine for most real life cases.
if you really want to stay with the effective length method, then you can compute k using an eigenvalue buckling feature of some analysis programs--sap2000 for example.  it's actually very easy to do this.
the dam is the way to go imo, though.  you'll know you did it "right" if you go that route.
this problem is addressed in "theory of elastic stability" by timoshenko and gere.
if the exact solution is unknown or very complicated, a method of successive approximations may be used.  a deflection curve for the column is first assumed.  based on these assumed deflections, the bending moments are calculated in terms of the axial force p.  knowing the bending moments, deflections are calculated by any of the standard methods.  equating the assumed deflections to the latter values gives an equation from which the critical load can be calculated.  the process is repeated, using the final set of deflections as a new approximation to the true values.
the process is repeated until there is very little difference between the assumed and calculated deflections in which case, the critical load is nearly exact.
at any point in the process, this procedure provides both an upper and lower bound to the critical load.  the process may be terminated when satisfactory precision has been achieved.
a worked example is given using n. m. newmark's numerical procedures for computing deflections.   
best regards,
ba